We present Chandra X-ray point source catalogs for 9 Hickson Compact Groups (HCGs, 37 galaxies) at distances of 34-89 Mpc. We perform detailed X-ray point source detection and photometry and interpret the point source population by means of simulated hardness ratios. We thus estimate X-ray luminosities (L(sub x)) for all sources, most of which are too weak for reliable spectral fitting. For all sources, we provide catalogs with counts, count rates, power-law indices (gamma), hardness ratios, and L(sub X), in the full (0.5-8.0 keV), soft (0.5-2.0 keV), and hard (2.0-8.0 keV) bands. We use optical emission-line ratios from the literature to re-classify 24 galaxies as star-forming, accreting onto a supermassive black hole (AGNs), transition objects, or low-ionization nuclear emission regions. Two-thirds of our galaxies have nuclear X-ray sources with Swift/UVOT counterparts. Two nuclei have L(sub X),0.5-8.0 keV > 10(exp 42) erg s-1, are strong multi-wavelength active galactic nuclei (AGNs), and follow the known alpha OX-?L? (nearUV) correlation for strong AGNs. Otherwise, most nuclei are X-ray faint, consistent with either a low-luminosity AGN or a nuclear X-ray binary population, and fall in the 'non-AGN locus' in alpha OX-?L? (nearUV) space, which also hosts other normal galaxies. Our results suggest that HCG X-ray nuclei in high specific star formation rate spiral galaxies are likely dominated by star formation, while those with low specific star formation rates in earlier types likely harbor a weak AGN. The AGN fraction in HCG galaxies with MR (is) less than -20 and L(sub X),0.5-8.0 keV (is) greater than 10(exp 41) erg s-1 is 0.08+0.35 -0.01, somewhat higher than the ~5% fraction in galaxy clusters.